Post navigation

I’ve really been happy to see how much my teaching skills have transferred to a business context. Employees are in some ways a lot like students. You need to teach them certain skills, motivate them to practice the things you teach them, and ideally, help them learn to be self-sufficient and improve themselves. When we have a new policy that we want to implement it, simply recognizing the implementation as a teaching-related challenge is a big step already. Then I try to use my teaching skills that I learned at LaGuardia and elsewhere to train employees, and even to help some employees learn how to train other employees.

I’ve been really enjoying my new job at Time Service in Toledo. I’m about to finish my third month here, and I expect I’ll be staying with this job for quite a while. I find that working in business gives me a variety of interesting problems to solve, and although they’re not deep and abstract in the same way as math research problems, they still require a lot of creative thinking and give me challenges to work on over time and puzzles to chew on as I drift off to sleep, in my morning shower, etc., just like math research did. The whole operation of helping to run a business feels like a big optimization problem — how do I figure out the best way to use all of our company’s resources to the greatest effect?

I hope all my friends in the New York Logic community are doing well. Please keep in touch!

I have resigned my position at LaGuardia Community College effective the beginning of the fall semester. I will be moving back to my birth town of Toledo, Ohio in a few days, where I will help to manage a medium-sized business started by my great-grandfather. It’s a watch repair business, with departments across the country. I’ll get to work closely with my father, who is the President of the company. I’m really looking forward to the opportunity to try out a completely different career.

As a side project, I hope to find some time to do a bit of research for MIRI. I’ve discussed MIRI research in a couple of recent posts here. I plan to continue updating this blog with stuff on MIRI research and other updates on my life. I’ll miss my colleagues in New York, and I hope we keep in touch. My students are welcome to keep in touch as well.

Here is a paper that came out of the MIRI Summer Fellows Program research workshop that I attended in June. The LaTeX code is here.

Quantilization is a form of mild optimization where you tell an AI to choose something at random from (for instance) the top 10% of best solutions, rather than taking the best solution. This helps to get around the problem of an agent whose values are mostly aligned with yours but that does pathological things when it takes its values to the extreme. In this paper, we examine a similar process, but involving two (or more) agents rather than one.

For those of you who were also at the MSFP, you can read some additional discussion of the paper here. The main idea is that Connor is working on a simulation to help test the ideas in the paper. If you’re interested in helping with the simulation but don’t have access to the forum post linked above, get in touch with me.

In June, I attended a two-week workshop in Northern California, combining technical research and personal growth. The workshop was run by the Machine Intelligence Research Institute (MIRI) and the Center For Applied Rationality (CFAR) in Northern California. The goal of MIRI is to lay the multidisciplinary theoretical foundations (in math, philosophy, computer science, and decision theory, among other fields) to try to insure friendly artificial intelligence, that is to say, to make it so that when artificial intelligence becomes smarter than humans, its interests are aligned with ours.

Their research has a fair amount of overlap with mathematical logic. I’d encourage any logicians who are interested in these sort of things to get involved. It’s a very good and important cause; the future of humanity is at stake. Unaligned artificial intelligence could destroy us all in a way that makes nuclear war and global warming seem tame in comparison.
Their technical research agenda is a good place to start for a technical perspective. The book Superintelligence by Nick Bostrom is a good starting point for a less technical introduction and to help understand why MIRI’s agenda is important and nontrivial.

One area of MIRI research that I find particularly interesting has to do with a version of Prisoner’s Dilemma played by computer programs that are allowed to read each others’ source code. This work makes use of a bounded version of Löb’s theorem. Actually, a fair bit of MIRI research relates to Löb’s theorem. Here is a good introduction.

Feel free to contact me if you’d like to know more about how to get involved with MIRI research. Or you can contact MIRI directly.

We submitted the infinite chess paper for publication a while back, but I forgot to post it.
The link below connects to a page that Joel wrote summarizing the key ideas, which also contains a link to the ArXiv for the full paper.

Today was my first day of teaching for the spring semester. I have a very different schedule this semester from last semester. Last semester, I had three courses, and I had requested that they be restricted to two days per week so that I wouldn’t have to come in as many days. In previous years at other institutions, that strategy had worked well to help me organize my time. However, I never taught more than two courses at once. Here at LaGuardia, teaching three long classes on the same day proved to be overwhelming, especially considering that I had to move my office hours to a third day and often ended up coming in a fourth day anyway to attend meetings, grade, prepare course materials, or do administrative work.

So I am happy that I have only one course each day this semester. I am teaching two courses this semester. Precalculus (Math 200) meets on Tuesdays and Thursdays at 8AM, and Elementary Algebra (Math 96) meets on Mondays and Wednesdays at 9:15 AM. (Each class meets with me a total of five hours per week.) Then on Fridays I have the set theory seminar at 10AM at the Graduate Center, or occasionally a faculty seminar at LaGuardia at 9AM where we will prepare to teach a seminar for first year LaGuardia students. I think that will be cool, because I really enjoyed my first year seminar as an undergraduate student at Grinnell.

This morning schedule is a big change for me; I have been a total night owl for the last seven years at least, rarely getting up much before noon. But I think it will be good for my health to wake up more with the sun. It might be a rough adjustment period, but it will be worthwhile. As a bonus, if all goes well, I can leave work by mid to late afternoon most days and be able to go out in the city some weekday evenings for dinner or a show. (If all doesn’t go well, I’ll be buried in grading, course preparation, administrative work, etc. and rarely get out of here until late anyway. But I am optimistic that it will be better than that.) Another nice benefit to the schedule is that I can conveniently make myself available for 45 minutes worth of office hours four days per week, so that students have a better opportunity to see me.

The elementary algebra students seem like a good group. They really seemed to appreciate the activity of sharing their feelings towards math and their expectations for the course. The videos didn’t seem to be as effective; only a few students commented on them, but the initial discussion before the videos was quite fruitful. A few students told me that they hate math, but many, I think a majority though I didn’t count, came in with positive attitudes towards math. Now it is my responsibility to help them to maintain these positive attitudes and to work hard and succeed in the class. I’m up for the challenge.

I recently started working with Joel Hamkins on a new project on infinite chess. We think that we will be able to improve on some results from his previous paper on transfinite game values in infinite chess to demonstrate a position with game value $\omega^4$. We made a lot of progress during January and February, as I was not teaching during that time. Teaching starts again for me next week. I hope that I will be able to find time to continue working on this project while I’m teaching during the spring semester. If not, then I will work on it more in the summer. Stay tuned to see a really cool infinite chess position 🙂

Last fall, I noticed that a major problem for many of my students, especially my basic students, was a lack of motivation to study math. So I spent a few hours today looking for some motivational articles and videos on the topic. I plan to show this motivational material to students on the first day of class (the spring semester starts in the beginning of March at LaGuardia) and then have them discuss it. Here’s the best of what I found: two videos and one article. If any of my readers have additional suggestions for motivational material, I’d be very interested. I think it’s really important to get students feeling motivated from the beginning of the semester.

Elementary epimorphisms were introduced by Philipp Rothmaler. A surjective homomorphism f: M –> N between two model-theoretic structures is an elementary epimorphism if and only if every formula with parameters satisfied by N is satisfied in M using a preimage of those parameters.

Philipp asked me whether nontrivial elementary epimorphisms between models of set theory exist. We answer this question in the negative for fully elementary epimorphisms between models of ZFC, but in the positive under weaker assumptions.

In particular, we show that every Pi_1-elementary epimorphism between models of ZF is an isomorphism. On the other hand, nonisomorphic Sigma_1-elementary epimorphisms between models of ZF can be constructed, as can fully elementary epimorphisms between models of ZFC^-.